After castling everything seems to be easy, still, since the prehistory of the game in fact isn't known , it isn't quite justified to suppose such a possibility - in circumstances of a real game the position most likely evidents that castling isn't available. It is but tricky

It must be one option saying if castle is avaliable or not.

Couldn't agree more.

I have to disagree with both understandings of a puzzle. A chess puzzle is simply a chess position with a forced mate. It's my understanding that the position need not be attainable through play of any kind, and so has neither prehistory nor theoretical possibility. That said, a "true" Chess position is described only by knowing whose turn it is, and whether castling or en passant are possible. So a true Chess position is (ironically) not the same as the position of the pieces on the board.

@bb_cb_love_pizza:
"it is a regulation for puzzles that castling is ALWAYS possible given the proper position of King and Rook"?
I've never heard of this, nor any entity assigning regulations on Chess puzzles. I'd be very interested know who/what says this. But I personally think that its a bad regulation to say the least, after all, if a puzzle is in print (like in the Westminster Gazette 96 years ago) you can't click on the piece and see if white can castle, and proving whether or not its possible that white can or cannot is computationally much harder than the problem in question.

@ sirissac

It is harder indeed, to prove the (im)possibility of moves like castling (and "en passant")
but there are some puzzles where the solution is fairly obvious in terms of finding mating moves if it wasnt for the problem of working out which of those moves is allowed and which ones are not.
For example i once saw a puzzle where you had to work out which one of your enemy pawns can be taken en passant to mate your opponent correctly (Using the wrong pawn would result in an impossible move and therefore be wrong, or would even make you lose the game).

You do not necessarily have to like that kind of a puzzle, if you dont like having to look at a problem that way, but that doesnt mean that it is a bad regulation, i know some people who enjoy those problems quite a lot because it forces you to approach the puzzle differently.

However, maybe i do not understand this quote correctly:
"But I personally think that its a bad regulation to say the least, after all, if a puzzle is in print (like in the Westminster Gazette 96 years ago) you can't click on the piece and see if white can castle"

That is exactly why there are regulations that work out whether it is possible or not. The cases of castling not being available are very, very rare however. With that said, the only problem for you will be to actually realize that king and rook are in position to castle.
And giving that away by a note (like "castling is possible")with the puzzle printed would most likely make the puzzle extremely trivial, as castling is not too often possible in Puzzles when not being part of the solution.

To those regulations and the example i mentioned above: Castling is ALWAYS possible unless proven not to be possible, en passant is NEVER possible unless it can be proven that the opposition moved that specific pawn being captured from rank 2 to rank 4 with his very last move.

it took this puzzle to get Lutz Neweklowski to create a puzzle that was not a mirror of the original. Because if he had mirrored this, White would not have been able to castle!